Kerodon

Corollary 7.1.8.14. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories, let $B$ be a simplicial set, and let $F^{B}: \operatorname{Fun}(B,\operatorname{\mathcal{C}}) \rightarrow \operatorname{Fun}(B, \operatorname{\mathcal{D}})$ be given by composition with $F$. If $\overline{f}: K^{\triangleright } \rightarrow \operatorname{Fun}(B,\operatorname{\mathcal{C}})$ is a levelwise $F$-colimit diagram (in the sense of Definition 7.1.8.13), then it is an $F^{B}$-colimit diagram.